{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:33:43Z","timestamp":1777703623905,"version":"3.51.4"},"reference-count":28,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2015,8,31]],"date-time":"2015-08-31T00:00:00Z","timestamp":1440979200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2015,8,31]]},"abstract":"<jats:p>\n                    In this paper, the notion of\n                    <jats:italic>M<\/jats:italic>\n                    -fuzzifying restricted hull operators is introduced and several equivalent characterizations are given. It is shown that there is a one-to-one correspondence between\n                    <jats:italic>M<\/jats:italic>\n                    -fuzzifying restricted hull operators and\n                    <jats:italic>M<\/jats:italic>\n                    -fuzzifying convex structures. As applications, some properties of the cut convex structures of an\n                    <jats:italic>M<\/jats:italic>\n                    -fuzzifying convex structure and of\n                    <jats:italic>M<\/jats:italic>\n                    -fuzzifying convexity preserving functions and of\n                    <jats:italic>M<\/jats:italic>\n                    -fuzzifying convex-to-convex functions are derived. In addition, using\n                    <jats:italic>M<\/jats:italic>\n                    -fuzzifying restricted hull operators, some\n                    <jats:italic>M<\/jats:italic>\n                    -fuzzifying convexities are naturally constructed from\n                    <jats:italic>M<\/jats:italic>\n                    -fuzzy quasi-orders.\n                  <\/jats:p>","DOI":"10.3233\/ifs-151765","type":"journal-article","created":{"date-parts":[[2016,1,15]],"date-time":"2016-01-15T12:23:29Z","timestamp":1452860609000},"page":"409-421","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":57,"title":["The restricted hull operator of\n                    <i>M<\/i>\n                    -fuzzifying convex structures"],"prefix":"10.1177","volume":"30","author":[{"given":"Fugui","family":"Shi","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China"}]},{"given":"Erqiang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China"},{"name":"School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, P.R. China"}]}],"member":"179","published-online":{"date-parts":[[2015,10,8]]},"reference":[{"key":"e_1_3_1_2_2","unstructured":"AsimowL. and EllisA.J. 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